For a large class of linear neutral type systems the problem of stabilizing feedback is studied. The proposed feedback is regular, in this sense that it does not contain the derivative of delayedâ€¦ (More)

Partial differential equations with discrete (concentrated) statedependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is notâ€¦ (More)

The functional differential equation of neutral type is studied. We consider the corresponding operator model in Hilbert space M2 = C n Ã— L2(âˆ’1, 0;C) and prove that there exists a sequence ofâ€¦ (More)

This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence ofâ€¦ (More)

1 IRCCyN, Ã‰cole des Mines de Nantes, 4 rue Alfred Kastler, 44307 Nantes, France. rabah@emn.fr 2 Institute of Mathematics, University of Szczecin, 70451 Szczecin, Wielkopolska 15, Poland.â€¦ (More)

We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions from a Banach spaceâ€¦ (More)

A new class of nonlinear partial differential equations with distributed in space and time state-dependent delay is investigated. We find appropriate assumptions on the kernel function whichâ€¦ (More)

We deal with a class of parabolic nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in biology. We first prove well-posedness in aâ€¦ (More)

A virus dynamics model with intracellular state-dependent delay and a general nonlinear infection rate functional response is studied. We consider the case of merely continuous solutions which isâ€¦ (More)

Stability properties of stationary solutions play a central role in the qualitative analysis of differential equations. There are many methods and approaches developed for different types ofâ€¦ (More)